Existence of positive solutions for a nonlinear quadratic integral equation

Date

2019-06-10

Authors

Wang, Chu-Hang
Ding, Hui-Sheng
N'Guerekata, Gaston

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation x(t) = g(t, x(t)) ∫t-∞ α(t, t - s) ƒ(s, x(s))ds, t ∈ ℝ. By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solution with positive infimum. An example illustrates the abstract result.

Description

Keywords

Quadratic integral equation, Positive solution, Cone

Citation

Wang, C. H., Ding, H. S., & N'Guerekata, G. M. (2019). Existence of positive solutions for a nonlinear quadratic integral equation. <i>Electronic Journal of Differential Equations, 2019</i>(79), pp. 1-11.

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Attribution 4.0 International

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